Question: Solve for $x$ and $y$ using elimination. $\begin{align*}x+9y &= 8 \\ 4x+6y &= 2\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $3$ $\begin{align*}-2x-18y &= -16\\ 12x+18y &= 6\end{align*}$ Add the top and bottom equations. $10x = -10$ Divide both sides by $10$ and reduce as necessary. $x = -1$ Substitute $-1$ for $x$ in the top equation. $ -1+9y = 8$ $-1+9y = 8$ $9y = 9$ The solution is $\enspace x = -1, \enspace y = 1$.